The analogue of the phase transition \(\rho ^*={2\over \alpha }-1\)  discussed in the context
of the largest clique problem takes place in the p-spin model as well
in the more extreme form called the chaos property: any non-trivial perturbation
of the instance \(J\)  whereby any fixed positive fraction of entries
of \(J\)  are flipped, results in the instance \(\tilde{J}\)  for which every near ground state is nearly
orthogonal to every near ground state of \(J\) . To put
it differently \(\rho ^*\)  is effectively zero for this model. This has been established in a series of
works [1]},[2]},[3]}.
Notably, the chaos property
itself is not a barrier to polynomial time algorithms since the Sherrington-Kirkpatrick model
is known to exhibit the chaos property, yet,
it is amenable to poly-time algorithms as in [4]} and [5]}.
The chaos property however is used as a tool to establish the ensemble version of the OGP (e-OGP) as
was done in [6]} and [7]}.
